Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have excelled in generating various objects, generating graphs remains challenging. This thesis explores the potential of score-based generative models in generating such objects through a modelization as combinatorial complexes, which are powerful topological structures that encompass higher-order relationships. In this thesis, we propose a unified framework by employing stochastic differential equations. We not only generalize the generation of complex objects such as graphs and hypergraphs, but we also unify existing generative modelling approaches such as Score Matching with Langevin dynamics and Denoising Diffusion Probabilistic Models. This innovation overcomes limitations in existing frameworks that focus solely on graph generation, opening up new possibilities in generative AI. The experiment results showed that our framework could generate these complex objects, and could also compete against state-of-the-art approaches for mere graph and molecule generation tasks.

利用图结构、生成模型、组合复杂体、随机微分方程和生成人工智能，提出了一个统一框架来生成复杂物体，包括图和分子，并且在这些任务上与最先进的方法相竞争。

通过随机微分方程进行基于组合复杂得分的扩散建模